Measurement of
J=ψ → Ξð1530Þ
−¯Ξ
+and evidence for the radiative decay
Ξð1530Þ
−→ γΞ
−M. Ablikim,1M. N. Achasov,10,dP. Adlarson,59S. Ahmed,15M. Albrecht,4M. Alekseev,58a,58cA. Amoroso,58a,58cF. F. An,1 Q. An,55,43Y. Bai,42O. Bakina,27R. Baldini Ferroli,23aI. Balossino,24aY. Ban,35K. Begzsuren,25J. V. Bennett,5N. Berger,26 M. Bertani,23aD. Bettoni,24a F. Bianchi,58a,58c J. Biernat,59J. Bloms,52I. Boyko,27R. A. Briere,5 H. Cai,60X. Cai,1,43 A. Calcaterra,23aG. F. Cao,1,47N. Cao,1,47S. A. Cetin,46b J. Chai,58c J. F. Chang,1,43W. L. Chang,1,47G. Chelkov,27,b,c
D. Y. Chen,6 G. Chen,1H. S. Chen,1,47J. C. Chen,1 M. L. Chen,1,43S. J. Chen,33Y. B. Chen,1,43W. Cheng,58c G. Cibinetto,24aF. Cossio,58cX. F. Cui,34H. L. Dai,1,43J. P. Dai,38,hX. C. Dai,1,47A. Dbeyssi,15D. Dedovich,27Z. Y. Deng,1
A. Denig,26I. Denysenko,27 M. Destefanis,58a,58c F. De Mori,58a,58c Y. Ding,31C. Dong,34 J. Dong,1,43L. Y. Dong,1,47 M. Y. Dong,1,43,47Z. L. Dou,33S. X. Du,63J. Z. Fan,45J. Fang,1,43S. S. Fang,1,47Y. Fang,1R. Farinelli,24a,24bL. Fava,58b,58c F. Feldbauer,4G. Felici,23a C. Q. Feng,55,43M. Fritsch,4 C. D. Fu,1Y. Fu,1 Q. Gao,1 X. L. Gao,55,43Y. Gao,45Y. Gao,56
Y. G. Gao,6Z. Gao,55,43 B. Garillon,26I. Garzia,24a E. M. Gersabeck,50 A. Gilman,51K. Goetzen,11L. Gong,34 W. X. Gong,1,43W. Gradl,26M. Greco,58a,58c L. M. Gu,33M. H. Gu,1,43S. Gu,2 Y. T. Gu,13A. Q. Guo,22L. B. Guo,32
R. P. Guo,36Y. P. Guo,26A. Guskov,27S. Han,60X. Q. Hao,16 F. A. Harris,48 K. L. He,1,47F. H. Heinsius,4 T. Held,4 Y. K. Heng,1,43,47M. Himmelreich,11,gY. R. Hou,47Z. L. Hou,1 H. M. Hu,1,47J. F. Hu,38,hT. Hu,1,43,47 Y. Hu,1 G. S. Huang,55,43 J. S. Huang,16 X. T. Huang,37 X. Z. Huang,33 N. Huesken,52T. Hussain,57W. Ikegami Andersson,59 W. Imoehl,22M. Irshad,55,43Q. Ji,1 Q. P. Ji ,16* X. B. Ji,1,47 X. L. Ji,1,43H. L. Jiang,37 X. S. Jiang,1,43,47X. Y. Jiang,34
J. B. Jiao,37Z. Jiao,18D. P. Jin,1,43,47 S. Jin,33Y. Jin,49T. Johansson,59N. Kalantar-Nayestanaki,29X. S. Kang,31 R. Kappert,29M. Kavatsyuk,29B. C. Ke,1 I. K. Keshk,4 A. Khoukaz,52P. Kiese,26R. Kiuchi,1 R. Kliemt,11 L. Koch,28 O. B. Kolcu,46b,fB. Kopf,4M. Kuemmel,4M. Kuessner,4A. Kupsc,59M. Kurth,1M. G. Kurth,1,47W. Kühn,28J. S. Lange,28 P. Larin,15L. Lavezzi,58cH. Leithoff,26T. Lenz,26C. Li,59Cheng Li,55,43D. M. Li,63F. Li,1,43F. Y. Li,35G. Li,1H. B. Li,1,47 H. J. Li,9,jJ. C. Li,1J. W. Li,41Ke Li,1 L. K. Li,1 Lei Li,3P. L. Li,55,43 P. R. Li,30Q. Y. Li,37W. D. Li,1,47W. G. Li,1
X. H. Li,55,43X. L. Li,37X. N. Li,1,43Z. B. Li,44Z. Y. Li,44H. Liang,55,43 H. Liang,1,47Y. F. Liang,40Y. T. Liang,28 G. R. Liao,12L. Z. Liao,1,47J. Libby,21C. X. Lin,44D. X. Lin,15Y. J. Lin,13B. Liu,38,hB. J. Liu,1C. X. Liu,1D. Liu,55,43 D. Y. Liu,38,h F. H. Liu,39Fang Liu,1 Feng Liu,6H. B. Liu,13H. M. Liu,1,47Huanhuan Liu,1 Huihui Liu,17J. B. Liu,55,43 J. Y. Liu,1,47K. Y. Liu,31Ke Liu,6 L. Y. Liu,13Q. Liu,47 S. B. Liu,55,43T. Liu,1,47X. Liu,30X. Y. Liu,1,47Y. B. Liu,34 Z. A. Liu,1,43,47Zhiqing Liu,37Y. F. Long,35X. C. Lou,1,43,47H. J. Lu,18J. D. Lu,1,47J. G. Lu,1,43Y. Lu,1 Y. P. Lu,1,43 C. L. Luo,32M. X. Luo,62P. W. Luo,44T. Luo,9,jX. L. Luo,1,43S. Lusso,58cX. R. Lyu,47F. C. Ma,31H. L. Ma,1L. L. Ma,37
M. M. Ma,1,47Q. M. Ma,1 X. N. Ma,34 X. X. Ma,1,47X. Y. Ma,1,43Y. M. Ma,37F. E. Maas,15M. Maggiora,58a,58c S. Maldaner,26S. Malde,53Q. A. Malik,57A. Mangoni,23b Y. J. Mao,35Z. P. Mao,1 S. Marcello,58a,58c Z. X. Meng,49
J. G. Messchendorp,29G. Mezzadri,24a J. Min,1,43 T. J. Min,33R. E. Mitchell,22 X. H. Mo,1,43,47 Y. J. Mo,6 C. Morales Morales,15N. Yu. Muchnoi,10,dH. Muramatsu,51A. Mustafa,4 S. Nakhoul,11,gY. Nefedov,27F. Nerling,11,g
I. B. Nikolaev,10,d Z. Ning,1,43S. Nisar,8,k S. L. Niu,1,43S. L. Olsen,47Q. Ouyang,1,43,47 S. Pacetti,23bY. Pan,55,43 M. Papenbrock,59P. Patteri,23a M. Pelizaeus,4H. P. Peng,55,43 K. Peters,11,g J. Pettersson,59J. L. Ping,32R. G. Ping,1,47 A. Pitka,4 R. Poling,51V. Prasad,55,43 H. R. Qi ,45† M. Qi,33T. Y. Qi,2 S. Qian,1,43C. F. Qiao,47N. Qin,60X. P. Qin,13 X. S. Qin,4Z. H. Qin,1,43J. F. Qiu,1S. Q. Qu,34K. H. Rashid,57,iK. Ravindran,21C. F. Redmer,26M. Richter,4A. Rivetti,58c V. Rodin,29M. Rolo,58c G. Rong,1,47Ch. Rosner,15M. Rump,52A. Sarantsev,27,e Y. Schelhaas,26K. Schoenning,59 W. Shan,19X. Y. Shan,55,43M. Shao,55,43C. P. Shen,2P. X. Shen,34X. Y. Shen,1,47H. Y. Sheng,1X. Shi,1,43X. D. Shi,55,43 J. J. Song,37Q. Q. Song,55,43 X. Y. Song,1S. Sosio,58a,58cC. Sowa,4S. Spataro,58a,58cF. F. Sui,37G. X. Sun,1J. F. Sun,16
L. Sun,60S. S. Sun,1,47 X. H. Sun,1 Y. J. Sun,55,43Y. K. Sun,55,43Y. Z. Sun,1 Z. J. Sun,1,43Z. T. Sun,1 Y. T. Tan,55,43 C. J. Tang,40G. Y. Tang,1 X. Tang,1 V. Thoren,59B. Tsednee,25I. Uman,46d B. Wang,1 B. L. Wang,47 C. W. Wang,33
D. Y. Wang,35K. Wang,1,43L. L. Wang,1 L. S. Wang,1 M. Wang,37M. Z. Wang,35 Meng Wang,1,47P. L. Wang,1 R. M. Wang,61W. P. Wang,55,43 X. Wang,35X. F. Wang,1 X. L. Wang,9,jY. Wang,55,43Y. Wang,44Y. F. Wang,1,43,47 Z. Wang,1,43 Z. G. Wang,1,43Z. Y. Wang,1 Zongyuan Wang,1,47 T. Weber,4 D. H. Wei,12P. Weidenkaff,26H. W. Wen,32 S. P. Wen,1U. Wiedner,4G. Wilkinson,53M. Wolke,59L. H. Wu,1L. J. Wu,1,47Z. Wu,1,43L. Xia,55,43Y. Xia,20S. Y. Xiao,1 Y. J. Xiao,1,47Z. J. Xiao,32Y. G. Xie,1,43Y. H. Xie,6 T. Y. Xing,1,47 X. A. Xiong,1,47Q. L. Xiu,1,43 G. F. Xu,1 J. J. Xu,33 L. Xu,1Q. J. Xu,14W. Xu,1,47X. P. Xu,41F. Yan,56L. Yan,58a,58cW. B. Yan,55,43W. C. Yan,2Y. H. Yan,20H. J. Yang,38,h H. X. Yang,1L. Yang,60R. X. Yang,55,43S. L. Yang,1,47Y. H. Yang,33Y. X. Yang,12Yifan Yang,1,47Z. Q. Yang,20M. Ye,1,43 M. H. Ye,7 J. H. Yin,1Z. Y. You,44B. X. Yu,1,43,47C. X. Yu,34J. S. Yu,20T. Yu,56C. Z. Yuan,1,47X. Q. Yuan,35Y. Yuan,1 A. Yuncu,46b,a A. A. Zafar,57Y. Zeng,20B. X. Zhang,1 B. Y. Zhang,1,43C. C. Zhang,1 D. H. Zhang,1 H. H. Zhang,44 H. Y. Zhang,1,43J. Zhang,1,47J. L. Zhang,61J. Q. Zhang,4 J. W. Zhang,1,43,47J. Y. Zhang,1 J. Z. Zhang,1,47K. Zhang,1,47 L. M. Zhang,45S. F. Zhang,33T. J. Zhang,38,hX. Y. Zhang,37Y. Zhang,55,43Y. H. Zhang,1,43Y. T. Zhang,55,43Yang Zhang,1
Yao Zhang,1Yi Zhang,9,jYu Zhang,47Z. H. Zhang,6Z. P. Zhang,55Z. Y. Zhang,60G. Zhao,1J. W. Zhao,1,43J. Y. Zhao,1,47 J. Z. Zhao,1,43Lei Zhao,55,43Ling Zhao,1M. G. Zhao,34Q. Zhao,1S. J. Zhao,63T. C. Zhao,1Y. B. Zhao,1,43Z. G. Zhao,55,43 A. Zhemchugov,27,bB. Zheng,56J. P. Zheng,1,43Y. Zheng,35Y. H. Zheng,47B. Zhong,32L. Zhou,1,43L. P. Zhou,1,47 Q. Zhou,1,47X. Zhou,60X. K. Zhou,47X. R. Zhou,55,43 Xiaoyu Zhou,20Xu Zhou,20A. N. Zhu,1,47 J. Zhu,34J. Zhu,44 K. Zhu,1 K. J. Zhu,1,43,47S. H. Zhu,54W. J. Zhu,34X. L. Zhu,45Y. C. Zhu,55,43Y. S. Zhu,1,47Z. A. Zhu,1,47J. Zhuang,1,43
B. S. Zou,1and J. H. Zou1 (BESIII Collaboration)
1Institute of High Energy Physics, Beijing 100049, People’s Republic of China 2
Beihang University, Beijing 100191, People’s Republic of China
3Beijing Institute of Petrochemical Technology, Beijing 102617, People’s Republic of China 4
Bochum Ruhr-University, D-44780 Bochum, Germany
5Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA 6
Central China Normal University, Wuhan 430079, People’s Republic of China
7China Center of Advanced Science and Technology, Beijing 100190, People’s Republic of China 8
COMSATS University Islamabad, Lahore Campus, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan
9
Fudan University, Shanghai 200443, People’s Republic of China
10G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia 11
GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
12Guangxi Normal University, Guilin 541004, People’s Republic of China 13
Guangxi University, Nanning 530004, People’s Republic of China
14Hangzhou Normal University, Hangzhou 310036, People’s Republic of China 15
Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
16Henan Normal University, Xinxiang 453007, People’s Republic of China 17
Henan University of Science and Technology, Luoyang 471003, People’s Republic of China
18Huangshan College, Huangshan 245000, People’s Republic of China 19
Hunan Normal University, Changsha 410081, People’s Republic of China
20Hunan University, Changsha 410082, People’s Republic of China 21
Indian Institute of Technology Madras, Chennai 600036, India
22Indiana University, Bloomington, Indiana 47405, USA 23a
INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy
23bINFN and University of Perugia, I-06100, Perugia, Italy 24a
INFN Sezione di Ferrara, I-44122, Ferrara, Italy
24bUniversity of Ferrara, I-44122, Ferrara, Italy 25
Institute of Physics and Technology, Peace Ave. 54B, Ulaanbaatar 13330, Mongolia
26Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany 27
Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
28Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut,
Heinrich-Buff-Ring 16, D-35392 Giessen, Germany
29KVI-CART, University of Groningen, NL-9747 AA Groningen, Netherlands 30
Lanzhou University, Lanzhou 730000, People’s Republic of China
31Liaoning University, Shenyang 110036, People’s Republic of China 32
Nanjing Normal University, Nanjing 210023, People’s Republic of China
33Nanjing University, Nanjing 210093, People’s Republic of China 34
Nankai University, Tianjin 300071, People’s Republic of China
35Peking University, Beijing 100871, People’s Republic of China 36
Shandong Normal University, Jinan 250014, People’s Republic of China
37Shandong University, Jinan 250100, People’s Republic of China 38
Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
39Shanxi University, Taiyuan 030006, People’s Republic of China 40
Sichuan University, Chengdu 610064, People’s Republic of China
41Soochow University, Suzhou 215006, People’s Republic of China 42
Southeast University, Nanjing 211100, People’s Republic of China
43State Key Laboratory of Particle Detection and Electronics,
Beijing 100049, Hefei 230026, People’s Republic of China
44Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China 45
46aAnkara University, 06100 Tandogan, Ankara, Turkey 46b
Istanbul Bilgi University, 34060 Eyup, Istanbul, Turkey
46cUludag University, 16059 Bursa, Turkey 46d
Near East University, Nicosia, North Cyprus, Mersin 10, Turkey
47University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China 48
University of Hawaii, Honolulu, Hawaii 96822, USA
49University of Jinan, Jinan 250022, People’s Republic of China 50
University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
51University of Minnesota, Minneapolis, Minnesota 55455, USA 52
University of Muenster, Wilhelm-Klemm-Str. 9, 48149 Muenster, Germany
53University of Oxford, Keble Rd, Oxford, United Kingdom OX13RH 54
University of Science and Technology Liaoning, Anshan 114051, People’s Republic of China
55University of Science and Technology of China, Hefei 230026, People’s Republic of China 56
University of South China, Hengyang 421001, People’s Republic of China
57University of the Punjab, Lahore-54590, Pakistan 58a
University of Turin, I-10125, Turin, Italy
58bUniversity of Eastern Piedmont, I-15121, Alessandria, Italy 58c
INFN, I-10125, Turin, Italy
59Uppsala University, Box 516, SE-75120 Uppsala, Sweden 60
Wuhan University, Wuhan 430072, People’s Republic of China
61Xinyang Normal University, Xinyang 464000, People’s Republic of China 62
Zhejiang University, Hangzhou 310027, People’s Republic of China
63Zhengzhou University, Zhengzhou 450001, People’s Republic of China
(Received 18 November 2019; published 8 January 2020)
The SU(3)-flavor violating decay J=ψ → Ξð1530Þ−¯Ξþþ c:c: is studied using ð1310.6 7.0Þ × 106 J=ψ events collected with the BESIII detector at BEPCII, and the branching fraction is measured to be BðJ=ψ → Ξð1530Þ−¯Ξþþ c:c:Þ ¼ ð3.17 0.02
stat 0.08systÞ × 10−4. This result is consistent with
pre-vious measurements with an order of magnitude improved precision. The angular parameter for this decay is measured for the first time and is found to beα ¼ −0.21 0.04stat 0.06syst. In addition, we report
evidence for the radiative decayΞð1530Þ−→ γΞ−with a significance of3.9σ, including the systematic uncertainties. The 90% confidence level upper limit on the branching fraction is determined to be BðΞð1530Þ−→ γΞ−Þ ≤ 3.7%. DOI:10.1103/PhysRevD.101.012004 *Corresponding author. jiqingping@htu.edu.cn †Corresponding author. qihongrong@tsinghua.edu.cn
aAlso at Bogazici University, 34342 Istanbul, Turkey.
bAlso at the Moscow Institute of Physics and Technology, Moscow 141700, Russia.
cAlso at the Functional Electronics Laboratory, Tomsk State University, Tomsk, 634050, Russia. dAlso at the Novosibirsk State University, Novosibirsk, 630090, Russia.
eAlso at the NRC“Kurchatov Institute”, PNPI, 188300, Gatchina, Russia. fAlso at Istanbul Arel University, 34295 Istanbul, Turkey.
gAlso at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany.
hAlso at Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education; Shanghai Key Laboratory for Particle Physics and Cosmology; Institute of Nuclear and Particle Physics, Shanghai 200240, People’s Republic of China.
iAlso at Government College Women University, Sialkot - 51310. Punjab, Pakistan.
jAlso at Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan University, Shanghai 200443, People’s Republic of China.
kAlso at Harvard University, Department of Physics, Cambridge, Massachusetts, 02138, USA.
Published by the American Physical Society under the terms of theCreative Commons Attribution 4.0 Internationallicense. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
I. INTRODUCTION
TheΞ and Ξð1530Þ hyperons are regarded as SU(3) octet (orbital angular momentum within quarks L ¼ 0 and spin-parity JP¼1
2þ) and decuplet (L ¼ 0 and JP¼32þ) baryons, respectively [1–3]. In this context, the process J=ψ → Ξð1530Þ−¯Ξþ [4] should be suppressed by the SU (3)-flavor symmetry[1,2,5]. Nevertheless, a sizable branch-ing fraction of ð5.9 1.5Þ × 10−4 [6,7] for the decay J=ψ → Ξð1530Þ−¯Ξþwas measured based onð8.6 1.3Þ × 106 J=ψ events by the DM2 Collaboration in 1982 and ð0.70 0.12Þ × 10−5 for the decay ψð3686Þ → Ξð1530Þ−¯Ξþbased onð448.1 2.9Þ × 106ψð3686Þ events by the BESIII Collaboration in 2019[8]. For comparison, the SU(3)-flavor violating decay J=ψ → Δþ¯p has a branching fraction of less than 1 × 10−4 [7] at 90% confidence level (C.L.), while the SU(3)-allowed decays J=ψ → p ¯p and J=ψ → Nð1535Þþ¯p [1] have branching fractions of ð1 − 2Þ × 10−3 [9]. Therefore, the branching fraction for J=ψ → Ξð1530Þ−¯Ξþ [7]is anomalously large when compared to that of J=ψ → Ξ−¯Ξþ, which is mea-sured to be ð0.98 0.08Þ × 10−3 [9]. An explanation for this anomaly is that a substantial JP ¼12− component may hide underneath the JP¼3
2þ peak while the branching fraction for J=ψ → Ξð1530Þ−¯Ξþwas obtained assuming a pure 32þ contribution around 1530 MeV=c2 [1]. An iso-doubletΞstate with JP¼1
2− around1520 MeV=c2[10], calledΞð1520Þ, is predicted in the diquark cluster picture, which is an SU(3) pentaquark octet with a ½ds½su¯u component. Due to the small number of event in the analysis of J=ψ → Ξð1530Þ−¯Ξþ reported by DM2 [7], it is difficult to give a solid conclusion on whether a12−partial wave contributes to the Ξð1530Þ mass region.
BESIII collected ð1310.6 7.0Þ × 106 J=ψ events
[11,12]in 2009 and 2012, a 2 orders of magnitude larger statistics than available to the DM2 experiment. A precision measurement with the BESIII experiment was therefore performed.
In 1981, Brodsky and Lepage [13] were the first to note the significance of angular distributions as a test of quantum chromodynamics. According to Ref. [13], the angular distribution of the J=ψ decay to a baryon-antibaryon (B ¯B) pair is defined by
dN
dcosθ∝ 1 þ αcos
2θ; ð1Þ
where θ is the polar angle between the baryon direction and the positron beam direction in the J=ψ rest frame, and α is a constant that parametrizes the angular distribution. The value of α has been predicted in many theoretical approaches for the SU(3)-allowed charmonium decays, such as electromagnetic contributions [14], quark mass effects [15,16], rescattering effects [17], etc. Considering electromagnetic contributions while ignoring quark mass
effects in the SU(3)-allowed J=ψ → B ¯B decays, the parameterα is expressed [14]as
α ¼m2J=ψ− 4M2B m2J=ψþ 4M2B;
where mJ=ψis the nominal J=ψ mass[9]and MBrefers to a baryon mass. Yet Carimalo[15]deemed that quark mass effects are more sensitive than electromagnetic contribu-tions to theα value. He provided the formula [15],
α ¼ð1 þ uÞ2− uð1 þ 6uÞ2 ð1 þ uÞ2þ uð1 þ 6uÞ2;
with u ¼ M2B=m2ψ (mψ denotes a charmonium resonance mass), which fits the experimental data better than when only considering electromagnetic effects. It is easy to see that 0 < α < 1 in the above-mentioned parametrizations. However, BESIII previously measured a negativeα values for J=ψ → Σ0¯Σ0and Σð1385Þ ¯Σð1385Þ [18,19]. Chen and Ping [17] investigated the rescattering effects of B ¯B in heavy quarkonium decays. As a result, the resulting angular distribution parameter α can be negative. However, there are no theoretical predictions or experimental data available on the angular distributions for SU(3)-flavor violating J=ψ decays. Measurements of angular distributions of such decays have the potential to bring more insight into the SU(3)-flavor violating mechanism.
In addition, the electromagnetic transition of decuplet to octet hyperons is a very sensitive probe of their structures
[3,20–22]. The partial width of the radiative transition Ξð1530Þ− → γΞ− is estimated to be 3.1 keV when con-sidering meson cloud effects with a relativistic quark model[3] in which the valence quark contributions for a baryon are supplemented by the pion or kaon cloud, and about 3 keV when considering octet-decuplet mixing with a nonrelativistic potential model [20]. Taking into account the total decay width of Ξð1530Þ− of 9.9 MeV [9], the branching fraction of Ξð1530Þ− → γΞ− is inferred to be about3.0 × 10−4. Experimentally, only an upper limit for BðΞð1530Þ−→ γΞ−Þ < 4% is reported at the 90% C.L. in 1975[23].
In this analysis, based on ð1310.6 7.0Þ × 106 J=ψ events [12] collected with the BEijing Spectrometer III (BESIII) at the Beijing Electron-Positron Collider (BEPCII), we measure the branching fraction of J=ψ → Ξð1530Þ−¯Ξþwith an improved precision and determine the angular distribution parameter for the first time. In addition, we also report evidence for the Ξð1530Þ− → γΞ− decay with a3.9σ significance based on the J=ψ → Ξð1530Þ−¯Ξþ process, and the corresponding 90% C.L. upper limit on the branching fraction is given.
II. BESIII DETECTOR AND MONTE CARLO SIMULATION
The BESIII detector operating at the BEPCII collider is described in detail in Ref. [24]. The detector is cylin-drically symmetric and covers 93% of4π solid angle. It consists of the following four subdetectors: a 43-layer main drift chamber (MDC), which is used to determine momenta of charged tracks with a resolution of 0.5% at 1 GeV=c in an axial magnetic field of 1 T with the 2009 data set and 0.9 T with the 2012 data set; a plastic scintillator time-of-flight system (TOF), with a time resolution of 80 ps (110 ps) in the barrel (end caps); an electromagnetic calorimeter (EMC) consisting of 6240 CsI(Tl) crystals, with relative photon energy resolution of 2.5% (5%) at 1 GeV in the barrel (end caps); and a muon counter consisting of 9 (8) layers of resistive plate chambers in the barrel (end caps), with a position resolution of 2 cm.
The response of the BESIII detector is modeled with Monte Carlo (MC) simulations using the software frame-workBOOST[25]based onGEANT4[26,27], which includes the geometry and material description of the BESIII detectors, the detector response and digitization models, as well as a database that keeps track of the running conditions and the detector performance. MC samples are used to optimize the selection criteria, evaluate the signal efficiency, and estimate backgrounds. Two signal MC samples of 0.3 million events each have been generated with the J2BB3 model [28] for the J=ψ → Ξð1530Þ−¯Ξþ reaction. The first MC sample contains inclusiveΞð1530Þ− decays and the second sample consists of exclusive Ξð1530Þ−→ γΞ− decay using the angular distribution constant α [see Eq.(1) of Ref. [28]] as measured in this analysis. Only the baryon decays ¯Ξþ → ¯Λπþand ¯Λ → ¯pπþ in the signal channels are simulated. An inclusive MC sample of 1.225 × 109 J=ψ events is used for the back-ground studies. Here, the J=ψ resonance is produced by means of the KKMC event generator [29], in which the initial state radiation is included. The decays are simulated by EVTGEN [30] with the known branching fractions taken from the Particle Data Group (PDG) [9], while the remaining unmeasured decay modes are generated with LUNDCHARM[31].
III. DATA ANALYSIS
A. J=ψ → Ξð1530Þ− ¯Ξ+ with Ξð1530Þ− → anything For the inclusive analysis of theΞð1530Þ−decay, a single tagged (ST) ¯Ξþ baryon candidate is reconstructed via ¯Λð→ ¯pπþÞπþ, while the Ξð1530Þ− candidate is treated as a missing particle. The presence of aΞð1530Þ−candidate is inferred using the mass recoiling against the ¯Λπþsystem, Mrecoil
¯Λπþ ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðE − E¯ΛπþÞ2− ðP¯ΛπþÞ2
p
, where E is the center-of-mass (c.m.) energy and ðE¯Λπþ; P¯ΛπþÞ is the four
momenta of the ¯Λπþ system in the eþe− rest frame. For signal candidate events, the distribution of Mrecoil
¯Λπþ will form
a peak around the nominal mass of the chargedΞð1530Þ− resonance[9].
Charged tracks must be properly reconstructed in the MDC with jcosθj < 0.93, where θ is the polar angle between the charged track and the positron beam direction. The combined information from the TOF and ionization loss (dE=dx) in the MDC is used to calculate particle identification confidence levels for each hadron (i) hypoth-esis (i ¼ p, π, K). A charged track is identified as the ith particle type with the highest confidence level. Events with at least one antiproton (proton) and two positively (neg-atively) charged pions are selected for tagging the ¯Ξþ (Ξ−) decay mode.
The ¯Λ candidates are reconstructed with a vertex fit to all the identified ¯pπþcombinations. A secondary vertex fit
[32]is then employed to the ¯Λ candidates, and events are kept if the decay length, i.e., the distance from the production vertex to the decay vertex, is greater than zero. If there remains more than one ¯pπþ combination in the event, the one closest to the nominal ¯Λ mass[9]is retained. A ¯Λ signal is required to have a ¯pπþ invariant mass within 5 MeV=c2 from the nominal ¯Λ mass [9]. The ¯Ξþ candi-dates are reconstructed via a secondary vertex fit by considering all combinations of the extra charged pions and the selected ¯Λ candidate, requiring that the decay length of the reconstructed ¯Ξþ candidates are greater than zero. If several combinations remain, the one with the minimumjM¯Λπþ− m¯Ξþj, where M¯Λπþis the invariant mass
of the ¯Λπþsystem and m¯Ξþ is the nominal mass of the ¯Ξþ
baryon [9], is selected. Additionally, the requirement jM¯Λπþ− m¯Ξþj ≤ 8 MeV=c2 is applied to further suppress
the backgrounds.
After applying the above selection criteria, a scatter plot of Mrecoil
¯Λπþ versus MST¯Λπþis shown in Fig.1(left), where MST¯Λπþ
is the ¯Λπþinvariant mass in the ST mode, and significantly clustered events of the SU(3)-flavor violating J=ψ → Ξð1530Þ−¯Ξþ decay are observed in the data. Figure 1 (middle) illustrates the distribution of MST
¯Λπþ. In both
figures, the red solid and green long-dashed lines indicate the ¯Ξþ signal and sideband regions, respectively. The Ξð1530Þ− signal in the Mrecoil
¯Λπþ spectrum has a
Breit-Winger shape, as shown in Fig.1(right).
The continuum data collected at the c.m. energy of 3.08 GeV, with an integrated luminosity of 30 pb−1
[11,12], are used to investigate the contribution from the quantum electrodynamics (QED) process eþe−→ Ξð1530Þ−¯Ξþ. By imposing the same event selection criteria as the J=ψ data, no events survived, meaning that the QED background is negligible. The contamination from the non- ¯Ξþ backgrounds is estimated with the ¯Ξþ mass side-band events, where the sideside-band regions are selected as
MST
¯Λπþ ∈ ½1.2817; 1.2977 ∪ ½1.3457; 1.3617 GeV=c2, as
indicated by the green long-dashed lines in Fig.1(middle). No peaking background is found in the Ξð1530Þ− signal region from the ¯Ξþmass sideband events, as indicated by the green-shaded histogram in Fig. 1 (right). The remaining backgrounds, investigated by the inclusive MC sample, form a smooth distribution in the Mrecoil
¯Λπþ spectrum in the region of
1.535 GeV=c2, where the main contributions are from J=ψ → Ξ−¯Ξþπ0 and J=ψ → Ξ0¯Ξþπ− events.
The signal yields of the J=ψ → Ξð1530Þ−¯Ξþ decay are extracted from an unbinned maximum likelihood fit to the Mrecoil
¯Λπþ spectrum. TheΞð1530Þ− signal is described by the
simulated MC shape convolved with a Gaussian function, which accounts for the mass resolution difference between the data and MC simulation. The mean of the Gaussian function is fixed to zero while the standard deviation is a free parameter. The background contribution is described by a second-order Chebychev polynomial function. The fit of the Mrecoil
¯Λπþ spectrum in data is shown in Fig.1(right), and
the fitted signal yields are listed in Table I.
B. J=ψ → Ξð1530Þ− ¯Ξ+ with Ξð1530Þ− → γΞ− The event selection criteria for the radiative decay Ξð1530Þ−→ γΞ− are based on the ¯Ξþ tagging mode.
Besides the tagged ¯Ξþ candidates described in Sec. III A, an extraΞ− baryon and a photon are selected to reconstruct the Ξð1530Þ− candidate. Since all decay particles from Ξð1530Þ− and ¯Ξþ are reconstructed from the J=ψ → Ξð1530Þ−¯Ξþ process, it is referred to as the double tag (DT) mode. The event selection ofΞ− candidates is similar to those of tagged ¯Ξþcandidates in Sec.III A, except for the charge-conjugated final states. The Ξ− candidate with the minimumjMDT
Λπ−− mΞ−j is the only one retained, and then is
requirement jMDTΛπ−− mΞ−j ≤ 8 MeV=c2 applied. The Ξ− mass window is shown by the red solid lines in Fig. 2
(left and middle), where MDT
Λπ− is the invariant mass of the
Λπ−system in the DT mode, and m
Ξ−is the nominal mass of
theΞ− baryon[9].
Photons are reconstructed by clustering the EMC crys-tals’ signals, and the energy deposited in the nearby TOF counter is included to improve the reconstruction efficiency and energy resolution[24]. A photon candidate is defined as a shower with an energy deposit of at least 25 MeV in the barrel region (jcosθ < 0.8j) or of at least 50 MeV in the end cap region (j0.86 < cosθj < 0.92). Showers in the angular range between the barrel and the end caps are poorly reconstructed and therefore excluded. An additional requirement on the EMC timing of a photon candidate, 0 ≤ t ≤ 700 ns, is employed to suppress electronic noise and energy deposits unrelated to the collision event, where time is measured relative to the event start time. All photons, which satisfy the above selection criteria are kept for further analysis.
A four-constraint (4C) kinematic fit is performed for events withγ, Ξ−, and ¯Ξþ candidates by imposing overall energy-momentum conservation. For each event, the com-bination with the lowest χ24C is selected. To suppress background events different from the final states of the signal channel, we requireχ24C< 5, which is determined by maximizing the figure-of-merit FOM¼ S=pffiffiffiffiffiffiffiffiffiffiffiffiS þ B. Here, S is the expected number of signal events from the signal MC simulation and B is the number of background events
TABLE I. Numerical results on the branching fraction meas-urement for J=ψ → Ξð1530Þ−¯Ξþ. The uncertainties are statistical only. Nobs ST 70186 544 NJ=ψ 1310.6 × 106 Bð ¯Ξ → ¯ΛπþÞ 99.89% Bð ¯Λ → ¯pπþÞ 63.90% ϵΞ− ST (ϵ¯Ξ þ ST) 24.03% (25.57%) f−(fþ) 1.079 0.011 (1.053 0.011) Branching fraction (×10−4) 3.17 0.02 ) 2 (GeV/c + π Λ ST M 1.28 1.29 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 ) 2 (GeV/c +π Λ recoil M 1.48 1.50 1.52 1.54 1.56 1.58 1.60 1.62 ) 2 (GeV/c + π Λ ST M 1.28 1.30 1.32 1.34 1.36 2 Events/0.1MeV/c 0 500 1000 1500 2000 2500 ) 2 (GeV/c + π Λ recoil M 1.48 1.5 1.52 1.54 1.56 1.58 1.6 1.62 2 Events/1MeV/c 0 500 1000 1500 2000 2500 3000 3500
FIG. 1. Left: scatter plot of Mrecoil
¯Λπþ versus MST¯Λπþ from the data, where MST¯Λπþ is the ¯Λπþinvariant mass in the ST mode. Middle: the MST
¯Λπþdistribution in the data. The red solid and green long-dashed lines indicate the ¯Ξþsignal and sideband regions, respectively. Right: fit to the experimental Mrecoil
¯Λπþ distribution. The red solid line is the fit result, the pink dotted line denotes the signal component, the blue long-dashed line represents the fitted background component, and the green-shaded histogram represents the normalized ¯Ξþ mass sideband events from the data.
from the inclusive MC sample in which the main back-ground processes (see below in the section) are known and normalized using PDG branching fraction values[9]. Three iterations between the S value and the χ24Crequirement are employed until the procedure is converged.
The γΞ− invariant mass spectrum of the events that remain after imposing the selection criteria above are shown in Fig. 2 (right). A weak enhancement of events in the region of the radiativeΞð1530Þ− decay can be seen. The background sources are divided into two categories, one with and one without theΞ− resonance. The non-Ξ− backgrounds are investigated by the Ξ− mass sideband events, where the sideband regions are defined as in the ST mode (see Sec.III A). It is found that very few events from the sidebands survived in the MγΞ− region around 1.535 GeV=c2. According to the inclusive MC informa-tion, the main background is the decay J=ψ → γηc→ γΞ−¯Ξþ, which distributes smoothly in the signal region of the Ξð1530Þ− baryon. Only a few peaking background events contributing to theΞð1530Þ mass region are found from the process J=ψ → Ξð1530Þ−¯Ξþ with Ξð1530Þ− decaying to the Ξ−π0 and Ξ0ð→ Λπ0Þπ− systems with a soft photon being undetected. Other background events, forming a flat distribution in theγΞ− mass spectrum, arise from the decays J=ψ → γΞ−¯Ξþ and J=ψ → Ξ−¯Ξþ.
The signal yields for the decay J=ψ → Ξð1530Þ−¯Ξþ→ γΞ−¯Ξþ are extracted by an unbinned maximum likelihood fit to the MγΞ− spectrum. The shape of the invariant mass
distribution of the Ξð1530Þ− baryon is modeled based on the prediction of the simulation. The few peaking back-ground events from the process J=ψ → Ξð1530Þ−¯Ξþ, with Ξð1530Þ− decaying to the Ξ−π0 and Ξ0ð→ Λπ0Þπ− sys-tems, are normalized with their branching fractions, where BðJ=ψ → Ξð1530Þ−¯ΞþÞ is obtained from this work and the branching fractions of twoΞð1530Þ− decays are from the PDG [9]. The smooth and dominating background from
J=ψ → γηc→ γΞ−¯Ξþ events is described by the MC-determined shape, where the corresponding number [9]
of the background events is normalized to the data. The remaining background shape is parametrized by an expo-nential function plus a first-order polynomial to describe the inclined flat slope in the MγΞ− distribution from the two main backgrounds, J=ψ → γΞ−¯Ξþand J=ψ → Ξ−¯Ξþ. The parameters of the exponential function and the first-order polynomial are fitted. The fit, shown in Fig.2(right), yields 33.2 9.6 signal events with a significance of 3.9σ which is the most conservative one among various fit scenarios (i.e., different fit range, signal shape, background shape, and background size). The significance is calculated from the test-statistic ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi−2 lnðL0=LmaxÞ
p
assuming Wilk’s theo-rem[33], whereLmaxandL0are the likelihoods of the fits with and without the Ξð1530Þ− signal included, respec-tively. The upper limit on the signal yield is determined by convolving the likelihood distribution with a Gaussian function with a standard deviation of σ ¼ x × Δ, where ) 2 (GeV/c + π Λ DT M 1.28 1.29 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 ) 2 (GeV/c -Ξγ M 1.45 1.50 1.55 1.60 1.65 ) 2 (GeV/c + π Λ DT M 1.28 1.30 1.32 1.34 1.36 2 Events/1MeV/c 0 5 10 15 20 25 30 35 40 ) 2 (GeV/c -Ξ γ M 1.45 1.50 1.55 1.60 1.65 2 Events/5MeV/c 0 2 4 6 8 10 12 14 16
FIG. 2. Left: scatter plot of MγΞ−versus MDT¯Λπþfrom the data, where MDT¯Λπþis the ¯Λπþinvariant mass spectrum in the DT mode. Middle: the MDT
¯Λπþdistribution from the data. The red solid and green long-dashed lines indicate the ¯Ξþsignal and sideband regions, respectively. Right: the fit to the experimental MγΞ−distribution. The red solid line is the fit result, the pink dotted line denotes the signal component, the cyan dash-dotted line describes the few peaking background events from the process J=ψ → Ξð1530Þ−¯ΞþwithΞð1530Þ−decaying to theΞ−π0andΞ0π−systems, the green long-dash-dotted line denotes the background events from J=ψ → γηc→ γΞ−¯Ξþ, and the blue
long-dashed line denotes the contribution from the remaining background events.
TABLE II. Systematic uncertainties on the branching fraction measurements. Here,Ξ−denotes theΞð1530Þ− resonance.
Source J=ψ → Ξ−¯Ξþð%Þ Ξ−→ γΞ−ð%Þ Photon 1.0 ¯Ξþefficiency correction 0.7 0.7 ¯Λ=Λ mass window 0.2 0.2 ¯Ξþ=Ξ− mass window 1.4 1.4 ¯Λ=Λ decay length 0.1 0.1 ¯Ξþ=Ξ− decay length 1.0 1.0 Kinematic fit 2.4 Angular distribution 0.5 3.6 Fit procedure 1.2 Intermediate decays 0.8 0.8 NJ=ψ 0.5 In total 2.5 4.9
x is the number of fitted signal events, and Δ refers to the total systematic uncertainty (4.9%, see TableII). It is found to be NULDT¼ 46 at the 90% C.L.
IV. MEASUREMENTS OF BRANCHING FRACTIONS AND ANGULAR DISTRIBUTION
A. Measurements ofBðJ=ψ → Ξð1530Þ− ¯Ξ+Þ andBðΞð1530Þ− → γΞ−Þ
The branching fraction for J=ψ → Ξð1530Þ−¯Ξþ is cal-culated using
BðJ=ψ → Ξð1530Þ−¯ΞþÞ ¼ NobsST
NJ=ψBð ¯ΞþÞBð ¯ΛÞϵST ; ð2Þ
where Nobs
ST is the number of events for ST, which is extracted from the fit to Mrecoil
¯Λπþ spectrum; NJ=ψ is the total number of J=ψ events [12]; Bð ¯ΞþÞ and Bð ¯ΛÞ are the
branching fractions [9] of ¯Ξþ→ ¯Λπþ and ¯Λ → ¯pπþ, respectively; ϵST, expressed as ðfþϵ¯Ξ
þ
STþ f−ϵΞ − STÞ=2, is the average detection efficiency in the ST mode for both the charge-conjugate processes, whereϵST¯ΞþðϵΞST−Þ denotes the MC-simulated efficiency for only tagging ¯ΞþðΞ−Þ decay mode, and fþðf−Þ is the correction factor for the ¯Ξþ (Ξ−) reconstruction efficiency estimated by using a control sample of J=ψ → Ξ−¯Ξþ with all polarization parameters considered. Here, fþðf−Þ is the ratio of the ¯Ξþ (Ξ−) reconstruction efficiency in the data [ϵdata¯Ξþ (ϵΞdata− )] to that in the MC sample [ϵMC¯Ξþ (ϵMCΞ− )], i.e., fþ¼ ϵdata¯Ξþ=ϵ¯Ξ
þ MC (f− ¼ ϵΞdata− =ϵΞ
−
MC). As a result, the branching fraction of BðJ=ψ → Ξð1530Þ−¯ΞþÞ is determined to be ð3.17 0.02Þ × 10−4 where the uncertainty is statistical only, and other numerical values are listed in TableI.
The upper limit at the 90% C.L. on the branching fraction for the radiative decayΞð1530Þ−→ γΞ− is calcu-lated using BULðΞð1530Þ−→ γΞ−Þ ¼ N UL DT NJ=ψBðJ=ψ → Ξð1530Þ−¯ΞþÞBð ¯ΞþÞBð ¯ΛÞBðΞ−ÞBðΛÞϵDT ¼ NULDTϵST BðΞ−ÞBðΛÞNobs STϵDT ; ð3Þ where NUL
DT is the upper limit on the number of fitted Ξð1530Þ−→ γΞ−signal events at the 90% C.L.;BðΞ−Þ and BðΛÞ are the branching fractions [9] of Ξ−→ Λπ− and Λ → pπ−, respectively;ϵ
DT, expressed as f−fþϵMCDT, is the detection efficiency in the DT mode, whereϵMC
DT denotes the MC-simulated efficiency using the J2BB3 model [28]. Taking the systematic uncertainty (see Sec. VA) into consideration, the upper limit at the 90% C.L. on the branching fraction ofΞð1530Þ−→ γΞ− is calculated to be 3.7%.
B. Measurement of the angular distribution inJ=ψ → Ξð1530Þ− ¯Ξ+
We obtain the number of recorded J=ψ → Ξð1530Þ−¯Ξþ events in each cosθ bin by fitting the ¯Λπþ invariant mass distribution as described in Sec.IVA. By dividing by the detection efficiency in each cosθ interval, we obtain the efficiency-corrected cosθ distribution shown in Fig. 3. A least square fit of Eq.(1)to the obtained cosθ distribution in the range of [−1.0, 1.0] gives α ¼ −0.20 0.04, where the uncertainty is statistical only.
V. SYSTEMATIC UNCERTAINTIES A. Branching fractions
The systematic uncertainties in the branching fraction measurements arise from many sources. They depend on the ¯Ξþ efficiency correction, mass windows for ¯Λ and ¯Ξþ, decay lengths for ¯Λ and ¯Ξþ, background shape, the amount
of background, the branching fractions of the intermediate decays, and the total number of J=ψ events. It is note-worthy that the uncertainties due to the tracking and particle identification efficiencies for the charged π track from the ¯Ξþ decay and the ¯Λ reconstruction efficiency are included in the charged ¯Ξþ reconstruction uncertainty. For the radiativeΞð1530Þ− decay they depend, in addition, on the photon reconstruction efficiency.
(1) Photon reconstruction efficiency: The uncertainty on the photon detection efficiency is 1.0% per photon,
θ cos -1 -0.5 0 0.5 1 Events/0.1 0 5000 10000 15000
FIG. 3. The cosθ distribution for J=ψ → Ξð1530Þ−¯Ξþ. The dots with error bars denote the efficiency-corrected data, and the red curve is the fit result.
obtained by studying J=ψ → ρ0π0, ρ0→ πþπ−, π0→ γγ events[34].
(2) ¯Ξþ efficiency correction: As mentioned above, the correction factor fþðf−Þ on the ¯Ξþ (Ξ−) recon-struction efficiency, defined asϵdata¯Ξþ =ϵMC¯Ξþ (ϵΞ
− data=ϵΞ
− MC), is obtained by using a control sample of J=ψ → ¯ΞþΞ−decays via single and double tag methods (the values are listed in Table I). The uncertainty on fþðf−Þ, obtained by adding the relative uncertain-ties for ϵdata¯Ξþ and ϵMC¯Ξþ (ϵΞdata− and ϵΞMC− ) in quadrature assuming the sources are independent, is found to be 1.0% for each mode. Therefore, the systematic uncertainty for ¯Ξþ efficiency correction is taken as 0.7% by averaging both charge-conjugate modes. (3) Mass window (decay length) of ¯Λ ( ¯Ξþ): The
uncertainty attributed to the ¯Λ ( ¯Ξþ) mass window (decay length) requirement is estimated using jεdata− εMCj=εdata, where εdata is the efficiency of applying the ¯Λ ( ¯Ξþ) mass window (decay length) requirement by extracting ¯Λ ( ¯Ξþ) signal in the ¯pπþ ( ¯Λπþ) invariant mass spectrum of the data, andεMCis the corresponding efficiency from the MC simulation. The difference between the data and the MC simu-lation is considered as the systematic uncertainty and is found to be 0.2% (0.1%) due to the ¯Λ mass window (decay length) requirement, and 1.4% (1.0%) for the
¯Ξþ mass window (decay length) requirement. (4) Kinematic fit for the radiativeΞð1530Þ−decay mode:
Correcting the tracking helix parameters[35]reduces the difference between MC simulation and data. The uncertainty of 2.4% due to the kinematic fit is estimated by the observed differences between an analysis that accounts for such correction and an analysis that does not. The correction factors obtained by control sample J=ψ → p ¯pπþπ− and gives 2.4% as the estimated systematic uncertainty.
(5) Angular distribution: The systematic uncertainty of angular distribution is estimated to take the larger difference of the detection efficiency by varying the measuredα values by 1σ in the MC simulation. And it is determined to be 0.5% and 3.6% for the inclusive and radiativeΞð1530Þ− decay modes, respectively. (6) Fit procedure: For the inclusive Ξð1530Þ− decay
mode, uncertainties due to the fitting range of Mrecoil ¯Λπþ
are estimated by changing the fitting range from 1.47–1.62 GeV=c2 to 1.475–1.615 GeV=c2 and 1.465–1.625 GeV=c2, respectively. The largest dif-ference with respect to the nominal value is 0.7%, and this is taken as the uncertainty associated with the fitting range. The uncertainty due to the background shape is estimated by changing the second-order polynomial function to a first-order polynomial. The relative difference on the signal yield of 1.0% is taken as the uncertainty due to the
background shape. In the fit of Mrecoil
¯Λπþ, the signal
shape is parametrized by the simulated MC shape convolved with a Gaussian function with the mean of zero. To estimate the uncertainty caused by a possible shift of the signal peak, an alternative model with the free mean of the Gaussian is used to estimate the uncertainty due to the signal shape. The difference between the two fits of 0.02% is negligible. Assuming that the sources above are independent and adding them in quadrature, the total systematic uncertainty associated with the fit pro-cedure is obtained to be 1.2%. As for the radiative Ξð1530Þ− decay mode, the uncertainty associated with the fit procedure is negligible since the nominal upper limit on BðΞð1530Þ− → γΞ−Þ is the most conservative one among multiple fit scenarios. (8) Intermediate decays: The uncertainties due to the
branching fractions of intermediate decays Ξ− → Λπ− and Λ → pπ− are 0.04% and 0.8% [9], re-spectively. Therefore, this uncertainty associated with the branching fractions of intermediate decays is taken to be 0.8%.
(9) Number of J=ψ events: The total number of J=ψ events is obtained by studying the inclusive hadronic J=ψ decays which has a systematic uncertainty of 0.5%[12].
Table II lists all systematic uncertainties on branching fraction measurements for the J=ψ → Ξð1530Þ−¯Ξþ decay in the ST mode and the radiativeΞð1530Þ− decay mode, respectively. The total systematic uncertainty is individu-ally calculated as the quadratic sum of all individual terms for each mode.
B. Angular distribution
The systematic uncertainties in the measurement of theα value arise from Mrecoil¯Λπþ fitting range, background shape,
cosθ fitting range, cosθ binning, and efficiency correction. It should be noted that the absolute value of the difference between the remeasuredα values in the alternative cases mentioned above and the nominal value is taken as the uncertainty given in this analysis.
(1) The Mrecoil
¯Λπþ fitting range: The uncertainty due to the
fitting range of Mrecoil¯Λπþ is estimated by changing the
fitting range from 1.47–1.62 GeV=c2 to 1.475– 1.615 GeV=c2 and 1.465–1.625 GeV=c2, respec-tively. The largest difference for αΞð1530Þ− of 0.02
is taken as the uncertainty due to the fitting range. (2) The background shape: The uncertainty due to the background shape in the angular distribution is estimated by changing the second-order polynomial function applied for fitting Mrecoil
¯Λπþ to a first-order
polynomial function. The difference becomes 0.04 forαΞð1530Þ−, and this is taken as the uncertainty due
(3) The cosθ fitting range: The uncertainty due to the cosθ fitting range is estimated by varying the cos θ fitting range to [−0.9, 0.9]. The difference on angular distribution is 0.01, and this is taken as the uncertainty due to the cosθ fitting range. (4) The cosθ binning: The uncertainty due to the
binning of cosθ is estimated by changing the nominal choice of 20 bins to 10 bins. The difference forα value between the two cases of 0.01 is taken as the systematic uncertainty due to the binning. (5) Efficiency correction: The α value is obtained by
fitting the efficiency-corrected cosθ distribution. To estimate the systematic uncertainty due to the MC generator to the fittedα value, the ratio of detection efficiencies between the data and MC simulation is obtained based on the process J=ψ → Ξð1530Þ−¯Ξþ with the inclusive decay of Ξð1530Þ−. The cosθ distribution is refitted using corrected one by the above ratio of detection efficiencies. The resulting absolute difference of 0.03 in α is taken as the systematic uncertainty due to the imperfection of MC simulation.
The absolute systematic uncertainties from the different sources for theα parameter of the angular distribution are given in Table III, and the total systematic uncertainty is obtained by adding the values in quadrature, assuming that the sources of uncertainty are independent.
VI. SUMMARY AND DISCUSSION
The SU(3)-flavor violating decay J=ψ → Ξð1530Þ−¯Ξþ is measured using ð1310.6 7.0Þ × 106 J=ψ events col-lected with the BESIII detector in 2009 and 2012. The signal is clearly observed (> 10σ), and the branching fraction is measured to beBðJ=ψ → Ξð1530Þ−¯Ξþþc:c:Þ ¼
ð3.170.020.08Þ×10−4. The result is consistent with the DM2 measurement [7] within 2 standard deviations (see TableIV), but with an order of magnitude improved precision. The α value of the angular distribution for J=ψ → Ξð1530Þ−¯Ξþ decay is measured for the first time and is found to beαΞð1530Þ¼ −0.21 0.04 0.06.
In addition, we present the first evidence for the Ξð1530Þ− → γΞ− radiative decay with a significance of 3.9σ. The upper limit at the 90% C.L. on the branching fraction of Ξð1530Þ− → γΞ− is measured to be 3.7%, which is consistent with the previous measurement [23]. The result is compatible with the theoretical prediction of 3.0 × 10−4 [3,20]. Our result provides complementary experimental information for isolating both the octet-decuplet mixing mechanism[20]and meson cloud effects
[3]in the baryon structure.
ACKNOWLEDGMENTS
The BESIII Collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. This work is supported in part by National Key Basic Research Program of China under Contract No. 2015CB856700; National Natural Science Foundation of China (NSFC) under Contracts No. 11565006, No. 11605042, No. 11625523, No. 11635010, No. 11735014, No. 11835012, No. 11935018; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; Joint Large-Scale Scientific Facility Funds of the NSFC and CAS under Contracts No. U1232107, No. U1532257, No. U1532258, No. U1732263, No. U1832207; CAS Key Research Program of Frontier Sciences under Contracts No. QYZDJ-SSW-SLH003, No. QYZDJ-SSW-SLH040; 100 Talents Program of CAS; INPAC and Shanghai Key Laboratory for Particle Physics and Cosmology; German Research Foundation DFG under Contract No. Collaborative Research Center CRC 1044; Istituto Nazionale di Fisica Nucleare, Italy; Koninklijke Nederlandse Akademie van Wetenschappen (KNAW) under Contract No. 530-4CDP03; Ministry of Development of Turkey under Contract No. DPT2006K-120470; National Science and Technology fund; The Knut and Alice Wallenberg Foundation (Sweden) under Contract No. 2016.0157; The Swedish Research Council; U.S. Department of Energy under Contracts No. DE-FG02-05ER41374, No. DE-SC-0010118, No. DE-SC-0012069; University of Groningen (RuG) and the Helmholtzzentrum fuer Schwerionenforschung GmbH (GSI), Darmstadt; China
TABLE III. Absolute systematic uncertainties on theα value.
Source αΞð1530Þ−
Mrecoil
¯Λπþ fitting range 0.02
Background shape 0.04
cosθ fitting range 0.01
cosθ binning 0.01
Efficiency correction 0.03
Total uncertainty 0.06
TABLE IV. Comparison of the results from this measurements to previous work.
This work Other measurements Theoretical prediction
BðJ=ψ → Ξð1530Þ−¯Ξþþ c:c:) (10−4) 3.17 0.02 0.08 5.9 0.9 1.2[7]
αðJ=ψ → Ξð1530Þ−¯ΞþÞ −0.21 0.04 0.06
Postdoctoral Science Foundation under Contract No. 2017M622347, Postdoctoral research start-up fees of Henan Province under Contract No. 2017SBH005, Ph.D research start-up fees of Henan Normal University
under Contract No. qd16164, Program for Innovative Research Team in University of Henan Province (Grant No. 19IRTSTHN018).
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